Uniqueness implies existence for discrete fourth order Lidstone boundary-value problems *

Johnny Henderson, Alvina Johnson
1999 unpublished
We study the fourth order difference equation u(m + 4) = f(m, u(m), u(m + 1), u(m + 2), u(m + 3)) , where f : Z×R 4 → R is continuous and the equation u5 = f (m, u1, u2, u3, u4) can be solved for u1 as a continuous function of u2, u3, u4, u5 for each m ∈ Z. It is shown that the uniqueness of solutions implies the existence of solutions for Lidstone boundary-value problems on Z. To this end we use shooting and topological methods.